CN105119858B

CN105119858B - Interference avoidance method based on constellation rotation in collaborative D2D Transmission systems

Info

Publication number: CN105119858B
Application number: CN201510431507.7A
Authority: CN
Inventors: 孙黎; 任品毅; 杜清河
Original assignee: Xian Jiaotong University
Current assignee: Xian Jiaotong University
Priority date: 2015-07-21
Filing date: 2015-07-21
Publication date: 2018-04-17
Anticipated expiration: 2035-07-21
Also published as: CN105119858A

Abstract

The present invention discloses an interference avoidance method based on constellation rotation in a cooperative D2D transmission system. The cooperative D2D transmission system includes a base station BS, two D2D users D ₁ and D ₂ and a cellular user CU. The implementation of the strategy The method is as follows: First, the signal constellation is rotated at each node and the channel phase information is pre-compensated, making full use of the inherent orthogonality between the in-phase component and the quadrature component of the complex signal to achieve interference-free transmission, thereby completely eliminating bit errors platform; on this basis, with the goal of maximizing the minimum square Euclidean distance, the constellation rotation angle is optimized and designed, which effectively reduces the symbol error rate of cellular communication and D2D communication. The simulation results show that the proposed strategy can reduce the symbol error rate of the system by two orders of magnitude compared with the traditional superposition coding strategy and the cooperative two-way transmission strategy.

Description

Interference avoidance method based on constellation rotation in cooperative D2D transmission system

The technical field is as follows:

the invention belongs to the technical field of wireless communication, and particularly relates to an interference avoiding method based on constellation rotation in a cooperative D2D transmission system.

Background art:

with the continuous emergence of new applications such as mobile multimedia, social networks, car networking and the like, the requirements of users on the service quality of communication systems are increasing day by day. However, conventional cellular communication techniques rely on a centralized network architecture, and mobile devices must communicate through base stations. In the case of a large number of devices and a large service request, this single communication mode may significantly increase the base station load and cause network congestion. For this purpose, a Device-to-Device (D2D) technique has been developed. In the D2D system, a mobile device with a short distance can directly perform point-to-point transmission without relaying through a base station, thereby effectively realizing the data distribution of the cellular network, improving the spectrum efficiency of the system, and expanding the coverage of the network. Due to the above advantages, the D2D technology has received general attention from both academia and industry, and is considered as one of the key technologies of the next generation cellular network.

In a cellular system supporting D2D communication, a direct link between devices and a transmission link between cellular users share the same spectrum, and therefore, how to achieve effective interference management is crucial to improve the performance of D2D communication. The existing interference management scheme mainly adopts resource allocation and signal processing technology to eliminate or weaken the influence of interference; and by establishing a cooperation mechanism, the mutual interference between the cellular link and the D2D link can be further alleviated, and the system performance can be improved. This is the basic idea of cooperative D2D transport. In this transmission mode, the transmitter of the D2D system acts as a relay node for the cellular link, assisting the cellular system in completing the end-to-end information transmission, thereby obtaining spectrum opportunities. As an instantiation of this idea, shalashi et al propose a superposition coding based collaborative D2D strategy in which the D2D transmitter transmits its own data and cellular user data simultaneously in superposition coding. To make more efficient use of transmission opportunities, Ma Chuan et al presents an improved cooperation scheme so that the D2D transmitter can relay only a portion of the cellular signal. The disadvantages of the two strategies are that: the spectral efficiency of both D2D and cellular transmissions is difficult to improve, subject to the double-hop nature of relay transmissions and node half-duplex constraints. To overcome this drawback, Pei Yiyang et al proposed a spectrally efficient cooperative bi-directional transmission strategy that enables a bi-directional connection to be established between a pair of D2D devices, while one of the D2D users acts as a relay to enable bi-directional information transfer between cellular users.

Although the above-mentioned cooperative bidirectional transmission strategy has high spectrum efficiency, the error code performance of the system is not satisfactory. Under the transmission framework of the strategy, signals received by any terminal comprise signals required by the terminal and signals sent to other users, so that the system is limited in interference, a serious error code platform can be caused, and the symbol error rate of the system cannot be reduced along with the increase of the signal-to-noise ratio. According to research, no relevant work has been done to solve this problem in the cooperative D2D transmission system.

The invention content is as follows:

the invention aims to provide an interference avoidance method based on constellation rotation in a cooperative D2D transmission system for eliminating an error code platform. By rotating the signal constellation and taking advantage of the inherent orthogonality between the in-phase and quadrature components of the complex signal, this strategy enables the construction of interference-free transmission links for both cellular and D2D communications, thereby avoiding interference altogether and eliminating error floor.

In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:

interference avoidance method based on constellation rotation in cooperative D2D transmission system, the cooperative D2D transmission system includes a base station BS, two D2D users D₁And D₂And a cellular subscriber CU, comprising the steps of:

1) before each transmission is started, signal constellation points of a base station BS, two D2D users and a cellular user CU are transmitted after signal constellation rotation operation;

2) each cooperative transmission between the D2D subsystem and the cellular subsystem in the cooperative D2D transmission system consists of two phases; wherein in the first phase the base station BS, the cellular user CU, the D2D user D₂Respectively transmit respective signals to D2D user D₁(ii) a In the second stage, D2D user D₁Forwarding a composite signal formed by combining signals of a base station BS and a cellular user CU, and realizing bidirectional information transmission between the cellular user CU and the base station BS; at the same time, D2D user D₁Transmitting its own signal to D2D user D₂(ii) a Finally, the base station BS, the cellular user CU and the D2D user D₂The detection of the signal and the acquisition of the information are all completed by adopting a maximum likelihood criterion.

The invention further improves that in the step 1), the design criterion of the rotation angle theta of the signal constellation is as follows:

in the formula:representing the minimum squared euclidean distance between constellation points of the transmitted signal.

A further improvement of the invention is that, for a base station BS or a cellular user CU,is defined asWherein x_CAndrespectively representing any two signal constellation points of the base station BS or the cellular user CU after the signal constellation is rotated; for D2D user D₁Or D₂，Is defined asWherein x_DAndrepresenting D2D user D₁Or D₂Any two signal constellation points after the signal constellation rotation.

A further improvement of the present invention is that the constellation rotation criterion is designed according to the following:

let u e x denote the original signal constellation, and the rotated signal constellation is denoted as x-e^jθu, where θ is a rotation angle, and its value is such that the in-phase component and the quadrature component of any two different constellation points in the rotated constellation set are different, that is: for any constellation point index number i ≠ k, all have

In the formula:representing any two constellation points in the rotated constellation set;

obviously, θ satisfying the above conditions is not unique, and therefore, a rotation angle capable of optimizing the system error performance is selected from θ; to this end, the SEP upper bound of the CU → BS link is expressed as SEP according to the joint bound, taking into account the cellular user's symbol error rate SEP first

In the formula:a set of values representing the original signal constellation,representation collectionPotential of (a), (b), (c), (d), (_CAndrepresenting any two signal constellation points after rotation of the signal constellation by the base station BS or cellular user CU, Q (x) represents a gaussian Q function,γ^(CU→BS)representing the received signal-to-noise ratio of the CU → BS link,representing a random variable gamma^(CU→BS)T represents an integral variable,is defined as

Likewise, D₁→D₂The SEP upper bound of the link is denoted as

In the formula:a set of values representing the original signal constellation,representation collectionT represents an integral variable, Q (x) represents a gaussian Q function,represents D₁→D₂The received signal-to-noise ratio of the link,representing random variablesProbability Density Function (PDF),is defined asWherein x_DAndrepresenting D2D user D₁Or D₂Any two signal constellation points after signal constellation rotation;

the above results show that in order to reduce the symbol error rate of link i → j, the transmitting node i selects a rotation angle that maximizes the least squares distance.

A further development of the invention is that in step 2) in the first phase the base station BS transmits a signalCellular subscriber CU signalsAnd D2D user D₂Transmitting a signalTo D2D user D₁Wherein: x is the number of_B、x_C、Respectively, base station BS, cellular user CU, D2D user D₂The complex constellation point after the signal constellation rotation; p denotes base station BS, cellular user CU, D2D user D₂The transmit power of (a); h is_B1Representing base station BS and D2D user D₁Channel coefficient between, h_C1Representing cellular subscribers CU and D2D subscriber D₁Channel coefficient between, h₁₂Representing D2D user D₁And D₂∠ h of the channel coefficient_B1、∠h_C1、∠h₁₂Respectively represent h_B1、h_C1、h₁₂The phase of (d); D2D user D₁The received signals are:

wherein,represents the first stage D₁Channel additive noise at a node; d₁Extraction ofAnd estimating the imaginary part by using the maximum likelihood criterionThen, the constellation is determined according to the one-to-one correspondence between the rotated constellation and its real or imaginary components given by the formula (2)Thus obtaining D2D user D₂The information of (a);

in detectingWhile, D is₁Extraction ofThereby obtaining a real part of

The further improvement of the invention is that in the step 2), the implementation process of the second stage is as follows: in the second stage, D2D user D₁Transmitting a signal of the form:

in the formula:is the power normalization factor that is used to normalize the power,is D2D user D₁To D2D user D₂The data of (a) to (b) to (c),is defined as shown in formula (6); thus, D2D user D₂The received signal is represented as

In the formula, h₁₂Representing the channel coefficients between D2D user D1 and D2,representing a second stage D2D, user D₂Channel additive noise of (a); to realize a pairDetection of D2D user D₂First, matched filtering is performed on a received signal, and then an imaginary part of the obtained signal is extracted to construct the following decision statistics:

D2D user D according to equation (9) and equation (2)₂Complete the processThereby recovering from the maximum likelihood detection；

The received signal of the base station BS is represented as

And D₂The operation is similar, the BS firstly usesMultiplying by the received signalThe real part is then extracted to obtain the following decision statistics:

in the formula:BS slaveMinusTo accomplish self-interference cancellation, we get:

based on equation (12), the base station BS completes the pairing using the maximum likelihood criterionAnd determining x according to the one-to-one correspondence between the rotated constellation and its real or imaginary components as given by equation (2)_CThereby obtaining information of the cellular subscriber CU;

the signal detection process performed by the cellular subscriber CU is the same as that performed by the base station BS given above.

The constellation rotation-based interference avoidance method provided by the invention has the following advantages:

firstly, by adopting the constellation rotation technology, the strategy can provide interference-free transmission conditions for the cellular link and the D2D link at the same time, thereby completely eliminating an error code platform and reducing the symbol error rate of the system.

Secondly, the only extra overhead introduced by the strategy is constellation rotation operation, and as can be seen from the above description, the constellation rotation angle is only related to the modulation mode adopted by the system, so that the overhead caused by constellation rotation can be ignored. This means that the proposed strategy has a low implementation complexity and is therefore very suitable for application in D2D communication systems.

Description of the drawings:

FIG. 1 is a schematic diagram of a system model;

FIG. 2 is a plot of symbol error rate for a CU → BS transmission link;

FIG. 3 is D₁→D₂A transmitted symbol error rate curve.

The specific implementation mode is as follows:

the invention is described in further detail below with reference to the accompanying drawings:

as shown in fig. 1, the interference avoidance method based on constellation rotation in the cooperative D2D transmission system of the present invention includes a base station BS, a cellular user CU, and 2D 2D users (denoted as D respectively)₁And D₂). There is a need for two-way communication between the base station BS and the cellular subscriber CU, but since they are far apart or are shielded by obstacles, no two-way transmission link can be established directly. And D2D user D₁And D₂Are two user equipments in close proximity, which want to utilize the terminal-through technology to achieve two-way information interaction. To satisfy D2D user D₁And D₂Of the base station BS allows D2D devices to multiplex the spectrum of the cellular network; in return, one device of the D2D device pair has to act as a relay to accomplish the bi-directional transmission between the base station BS and the cellular user CU. Without loss of generality, assume D2D user D₁As a relay node. It is assumed that all nodes are configured with a single antenna and operate in half-duplex mode. Let the transmit power of each node be P, and represent the additive noise at each receiver as zero mean with variance N₀Complex gaussian random variables.

In the proposed strategy, the signal constellation points of all nodes are transmitted after being rotated, and the specific manner of rotation is as follows:

order toRepresenting the original signal constellation, the rotated signal can be represented as x ═ e^jθu, where θ is a rotation angle, and its value should be such that the in-phase components (and quadrature components) of any two different constellation points in the rotated constellation set are different. Namely: for any i ≠ k, all

WhereinRepresenting any two constellation points in the rotated constellation set. Obviously, θ satisfying the above conditions is not unique, and therefore, it is desirable to select a rotation angle from them that can optimize the system error performance. For this purpose, the SEP upper bound of the CU → BS link is expressed as SEP upper bound according to the joint bound, taking into account the symbol error rate (SEP) of the cellular user first

In the formula:a set of values representing the original signal constellation,representation collectionPotential of (a), (b), (c), (d), (_CAndrepresenting any two signal constellation points after rotation of the signal constellation by the base station BS or cellular user CU, Q (x) represents a gaussian Q function,γ^(CU→BS)representing the received signal-to-noise ratio of the CU → BS link,representing a random variable gamma^(CU→BS)A Probability Density Function (PDF), t represents an integral variable,is defined as

Likewise, D₁→D₂The SEP upper bound of the link is denoted as

the above results show that in order to reduce the symbol error rate of link i → j, the transmitting node (node i) should select a rotation angle that maximizes the least square distance, i.e. the rotation angle should be designed according to the criteria given in equation (1).

By performing theoretical analysis on the upper bound of the symbol error rates of the cellular users and the D2D users, for any transmitting node, the rotation angle capable of maximizing the minimum square distance should be selected, that is, the rotation angle should satisfy:

in the formula:representing the minimum squared euclidean distance between constellation points of the transmitted signal. For a base station BS or a cellular user CU,is defined asWherein x_CAndrepresents any two signal constellation points after the base station BS or the cellular user CU has been rotated by the signal constellation; for D2D user D₁Or D₂，Is defined asWherein x_DAndrepresenting D2D user D₁Or D₂Any two signal constellation points after the signal constellation rotation.

Each cooperation between the D2D system and the cellular system (i.e., each cooperation period) consists of two phases. In the first phase, base station BS, cellular subscriber CU, D2D user D₂Respectively transmit respective signals to D2D user D₁. In the second stage, D2D user D₁Forwarding a signal formed by combining information of a base station BS and information of a cellular user CU, so as to realize bidirectional information transmission between cellular users; at the same time, D2D user D₁Also transmits its own signal to D2D user D₂。

In the first phase, the base station BS transmitsWherein x_BWhich represents the complex constellation points after rotation at the BS side of the base station. It is assumed here that the average power of the real part of the constellation points is normalized, i.e.:this assumption is also true in the following discussion. Similarly, cellular subscribers CU and D2D subscriber D₂The transmitted signals are respectively represented asAndthus, D2D user D₁The received signals are:

in the formula:represents the first stage D₁Channel additive noise at a node. In the following description we useRepresenting the channel noise at node n of the mth stage. D2D user D₁Extraction ofAnd estimating the imaginary part by using the maximum likelihood criterionAccording to the design rule of the rotation angle of the constellation, the rotated constellation and the real (imaginary) component thereof have one-to-one correspondence, so thatCan be completely composed ofResume, whereby D2D user D₁Able to obtain D2D user D₂The information of (1). In detectingWhile, D is₁Extraction ofThereby obtaining a real part of

In the second stage, D2D user D₁The messages of the base station BS and the cellular subscriber CU need to be forwarded to complete the two-way communication between the cellular subscribers; at the same time, it also needs to transmit its own information to D2D user D₂. To this end, we design D2D user D₁The transmitted signal has the following form:

in the formula:is the power normalization factor that is used to normalize the power,is D2D user D₁To D2D user D₂The data of (1). Thus, D2D user D₂The received signal may be represented as

To realize a pairDetection of D2D user D₂First, matched filtering is performed on a received signal, and then an imaginary part of the obtained signal is extracted to construct the following decision statistics:

based on equation (9), D2D user D₂Can completeThereby recovering from the maximum likelihood detection

The received signal at the BS end of the base station can be expressed as

And D2D user D₂The operation is similar, the base station BS uses firstlyMultiplying by the received signalThe real part is then extracted to obtain the following decision statistics:

in the formula:due to the fact thatIs the signal sent by the base station BS in the previous stage, the base station BS can firstMinusTo accomplish self-interference cancellation and then detection based on the remaining part as shown in equation (12)(equivalent to detecting x)_C)：

Similar to the above analysis, the received signal at the cellular user CU side can be expressed as:

based on the received signal, x_BCan be recovered. Since the signal detection process performed by the cellular subscriber CU and the base station BS are substantially identical, specific details are omitted.

To verify the performance of the strategy proposed by the present invention, we performed the following computer simulations:

in the simulation, we assume that all nodes are distributed in a two-dimensional plane. Without loss of generality, assume a base station BS, a cellular user CU, two D2D users D₁And D₂Respectively located at (0,0), (1,1), (0.5 ) and (1, 0). The channel coefficients between nodes obey a complex gaussian random distribution model, namely:suppose thatWherein d is_ijIt is the distance between nodes i and j, η is the path loss index, unless otherwise specified, each node in the following simulation uses QPSK as the modulation mode, it can be calculated according to equation (1), at this time, the constellation rotation angle of each node should be selected to be 26.56 °.

Fig. 2 shows the simulation results of the symbol error rate of the cellular user (i.e., CU → BS transmission). As can be seen from fig. 2, both reference strategies have a significant error floor, that is, the symbol error rate of the system does not decrease with the rise of the signal-to-noise ratio. This is caused by the interference limited nature of both strategies. In contrast, the proposed strategy of the present invention can completely avoid interference, so the SEP of the system will decrease rapidly with increasing SNR.

FIG. 3 depicts a D2D user (i.e., D:. D)₁→D₂Link) of the link. As expected, the SEP of the cooperative bi-directional transmission strategy does not improve with increasing SNR. The superposition coding strategy can achieve significant performance gains at medium to high signal-to-noise ratios compared to the cooperative bi-directional transmission strategy, because the superposition coding strategy allows for a D2D receiver (i.e., D2D receiver)₂) In the first stage, the signals of the cellular subscriber CUs are coded so that D2D subscriber D ends at the end of the second stage₂The signal of the cellular user CU can be first cancelled and then the own data decoded, thus attenuating the effect of the cellular user interference. However, the superposition coding strategy still exhibits significant performance compared to the strategy proposed by the present inventionThis is disadvantageous because in the superposition coding strategy, D2D user D₂Errors may occur in the decoding at the first stage, resulting in D2D user D at the end of the second stage₂The interference cancellation of (2) is unsuccessful. Unlike superposition coding strategies and cooperative bi-directional transmission strategies, the proposed strategy achieves the objective of completely avoiding interference by using constellation rotation techniques, and therefore has the best performance among several comparison schemes.

Claims

1. Interference avoidance method based on constellation rotation in a cooperative D2D transmission system, characterized in that the cooperative D2D transmission system comprises a base station BS, two D2D users D₁And D₂And a cellular subscriber CU, comprising the steps of:

1) before each transmission is started, signal constellation points of a base station BS, two D2D users and a cellular user CU are transmitted after signal constellation rotation operation; the design criterion of the signal constellation rotation angle theta is as follows:

<mrow> <mi>&theta;</mi> <mo>=</mo> <mi>arg</mi> <mi>max</mi> <mi> </mi> <msubsup> <mi>d</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

in the formula:representing the minimum squared euclidean distance between constellation points of the transmitted signal;

for a base station BS or a cellular user CU,is defined asWherein x_CAndrespectively representing any two signal constellation points of the base station BS or the cellular user CU after the signal constellation is rotated; for D2D user D₁Or D₂，Is defined asWherein x_DAndrepresenting D2D user D₁Or D₂Any two signal constellation points after signal constellation rotation; wherein, the markThe representation takes the real part, i.e.:denotes x_CThe real part of (a) is,to representThe real part of (a) is,denotes x_DThe real part of (a) is,to representThe real part of (a);

2. The method for interference avoidance based on constellation rotation in a cooperative D2D transmission system according to claim 1, wherein the constellation rotation criterion is designed according to the following:

order toRepresenting the original signal constellation, the rotated signal constellation is denoted x ═ e^jθu, where θ is a rotation angle, and its value is such that the in-phase component and the quadrature component of any two different constellation points in the rotated constellation set are different, that is: for any constellation point index number i ≠ k, all have

In the formula:representing any two constellation points in the rotated constellation set,denotes xⁱThe imaginary part of (a) is,denotes x^kAn imaginary part of (d);

<mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mi>E</mi> <mrow> <mo>(</mo> <mi>C</mi> <mo>)</mo> </mrow> </msubsup> <mo>&le;</mo> <mfrac> <mn>1</mn> <mrow> <mo>|</mo> <mi>&chi;</mi> <mo>|</mo> </mrow> </mfrac> <munder> <munder> <mo>&Sigma;</mo> <mrow> <msub> <mi>x</mi> <mi>C</mi> </msub> <mo>,</mo> <mover> <msub> <mi>x</mi> <mi>C</mi> </msub> <mo>^</mo> </mover> <mo>&Element;</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mi>&theta;</mi> </mrow> </msup> <mi>&chi;</mi> </mrow> </munder> <mrow> <mover> <msub> <mi>x</mi> <mi>C</mi> </msub> <mo>^</mo> </mover> <mo>&NotEqual;</mo> <msub> <mi>x</mi> <mi>C</mi> </msub> </mrow> </munder> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>&infin;</mi> </msubsup> <mi>Q</mi> <mrow> <mo>(</mo> <msqrt> <mfrac> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>C</mi> <mo>,</mo> <mover> <mi>C</mi> <mo>^</mo> </mover> </mrow> <mn>2</mn> </msubsup> <mi>t</mi> </mrow> <mn>4</mn> </mfrac> </msqrt> <mo>)</mo> </mrow> <msub> <mi>f</mi> <msup> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>C</mi> <mi>U</mi> <mo>&RightArrow;</mo> <mi>B</mi> <mi>S</mi> <mo>)</mo> </mrow> </msup> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&le;</mo> <mrow> <mo>(</mo> <mo>|</mo> <mi>&chi;</mi> <mo>|</mo> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>&infin;</mi> </msubsup> <mi>Q</mi> <mrow> <mo>(</mo> <msqrt> <mfrac> <mrow> <msubsup> <mi>d</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mi>t</mi> </mrow> <mn>4</mn> </mfrac> </msqrt> <mo>)</mo> </mrow> <msub> <mi>f</mi> <msup> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>C</mi> <mi>U</mi> <mo>&RightArrow;</mo> <mi>B</mi> <mi>S</mi> <mo>)</mo> </mrow> </msup> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

Likewise, D₁→D₂The SEP upper bound of the link is denoted as

<mrow> <msubsup> <mi>P</mi> <mi>E</mi> <mrow> <mo>(</mo> <mi>C</mi> <mo>)</mo> </mrow> </msubsup> <mo>&le;</mo> <mrow> <mo>(</mo> <mo>|</mo> <mi>&chi;</mi> <mo>|</mo> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>&infin;</mi> </msubsup> <mi>Q</mi> <mrow> <mo>(</mo> <msqrt> <mfrac> <mrow> <msubsup> <mi>d</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mi>t</mi> </mrow> <mn>4</mn> </mfrac> </msqrt> <mo>)</mo> </mrow> <msub> <mi>f</mi> <msup> <mi>&gamma;</mi> <mrow> <mo>(</mo> <msub> <mi>D</mi> <mn>1</mn> </msub> <mo>&RightArrow;</mo> <msub> <mi>D</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </msup> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

3. The interference avoidance method based on constellation rotation in cooperative D2D transmission system according to claim 2, wherein in step 2), the BS sends signal in the first phaseCellular subscriber CU signalsAnd D2D user D₂Transmitting a signalTo D2D user D₁Wherein: x is the number of_B、x_C、Individual watchBase station BS, cellular user CU, D2D user D₂The complex constellation point after the signal constellation rotation; p denotes base station BS, cellular user CU, D2D user D₂The transmit power of (a); h is_B1Representing base station BS and D2D user D₁Channel coefficient between, h_C1Representing cellular subscribers CU and D2D subscriber D₁Channel coefficient between, h₁₂Representing D2D user D₁And D₂∠ h of the channel coefficient_B1、∠h_C1、∠h₁₂Respectively represent h_B1、h_C1、h₁₂The phase of (d); D2D user D₁The received signals are:

in detectingWhile, D is₁Extraction ofThereby obtaining a real part of

4. The method for interference avoidance based on constellation rotation in a cooperative D2D transmission system as claimed in claim 2, wherein the second stage is implemented as follows in step 2): in the second stage, D2D user D₁Transmitting a signal of the form:

D2D user D according to equation (9) and equation (2)₂Complete the processThereby recovering from the maximum likelihood detection

The received signal of the base station BS is represented as